. General Form of a Straight Line The linear equation (first degree polynomial in two variables x and y ) ax by = (where a, b and c are real numbers such that at least one of a, b is non-zero) always represents a straight line. This is the general form of a straight line. Now, let us find out the equations of a straight line in the following cases (i) parallel to ax + by + c = (ii) perpendicular to ax + by + c = .
. Equation of a line parallel to the line ax by = The equation of all lines parallel to the line ax by = can be put in the form ax by k = for different values of k . . .
Equation of a line perpendicular to the line ax by = The equation of all lines perpendicular to the line ax by = can be written as bx ay k = for different values of k . Coordinate Geometry Two straight lines a x b y and a x b y where the coefficients are non-zero, are (i) parallel if and only if a ; That is, a b a b (ii) perpendicular if and only if a a b b Progress Check Fill the details in respective boxes No. Equations Parallel or perpendicular S.No. Equations Parallel or perpendicular x – y + = .
. Slope of a straight line The general form of the equation of a straight line is ax by = . (at least one of a , b is non-zero) coefficient of x , coefficient of y , constant term = c . The above equation can be rewritten as by = − ax gives y = − b x b , if b ¹ … ( ) comparing ( ) with the form y mx l We get, slope m = − a